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Primel Time Units
Fundamental Reality: The Mean Solar Day The ′Timel (or ′Jiffy) The mean solar day is a fundamental reality of human life. Accordingly, Primel uses a simple dozenal power of the day, the hexciaday (z|10-6 days) as its base unit of time, the ′timel. This comes out to d|50/1728 or d|1/34.56 of a second (z|0.042 s, or d|0.02893518 s), making this quite a fleeting moment of time, a bit shorter than the frame period for typical movie film, and hence just beyond human perception. This happens to be very close to the vibration period for a C♯0 musical note. For this reason, dozenalists in the past have called this a "vic" (short for "vi-bration of C"). However, perhaps we can do better than this, and find an existing English word that captures how transitory this unit is: Primel proposes to nickname this the ′jiffy. Although the ′jiffy is a very short interval indeed, it is nevertheless a useful quantity for precision scientific and engineering purposes. Not to mention sports, especially the Olympic variety, where a down-to-the-′jiffy time might mean the difference between a medal made of bronze or silver, and one of gold! In any event, given the principle of 1:1 correspondence of base units Primel adheres to, this sizing for the ′timel will have interesting effects on the rest of the units in the metrology. The ′Unquatimel (or ′Twinkling) On the other hand, the unqual powers of the ′timel do fall within the range of human perception, starting with the ′unquatimel (z|101 ′timels). This is equivalent to the pentciaday (z|10-5 days), which comes out to d|50/144 of a second (z|0.42 s, or d|0.3472 s). In the past, dozenalists have dubbed this unit the "dovic" (short for "a dozen vics"). But perhaps we can find a nickname that is a little more intuitive. Note that this unit is a little over a third of a second, and therefore about the time it takes to blink an eye. Accordingly, Primel proposes to colloquialize this unit as the ′twinkling. So a dozen ′jiffies make a ′twinkling. The ′Biquatimel (or ′Waltzing) The ′biquatimel (z|102 ′timels) is equivalent to the quadciaday (z|10-4 days). This comes out to d|50/12 of a second (z|4.2 s, or d|4.16 s). In the past, dozenalists have called this unit the "grovic" (short for "a gross of vics"). Again, let's see if we can be a bit more creative. A ′biquatimel counts out a dozen ′twinklings in slightly over four seconds. If these were beats of music, then it would correspond to 4 measures of 3/4 musical time at d|172.8 beats per minute, an Allegro Vivace tempo. This is enough, for example, to express the melodic theme of a typical Viennese waltz (such as Strauss's Blue Danube). Hence, Primel proposes to nickname this interval a ′waltzing. The ′Triquatimel (or ′Brevit) The ′triquatimel (z|103 ′timels) is equivalent to the triciaday (z|10-3 days). This comes out to exactly d|50 seconds (z|42 s), which makes it a minute-like quantity, although a bit shorter. For that reason, dozenalists in the past have suggested naming this a "minette". However, perhaps we could find a name that is a little less beholden to the ancient Babylonian sexagesimal system. Primel proposes to nickname this unit the ′brevit. This is short for "brevity", conveying the sense that this is a brief period of time, and a little briefer than the minute, which it rhymes with. So a ′brevit consists of a dozen ′waltzings. It is exactly intermediate on the logarithmic scale between the day and the ′timel: A day consists of z|1000 (d|1728) ′brevits, and a ′brevit consists of z|1000 (d|1728) ′jiffies. The ′Quadquatimel (or ′Segment) The ′quadquatimel (z|104 ′timels) is equivalent to the biciaday (z|10-2 days). This comes out to exactly d|600 seconds (z|420 s), or ten minutes. This is equivalent to a dozen ′brevits. It's interesting to note that, the decimal figure for "d|10 minutes" resembles the equivalent dozenal figure for "z|10 ′brevits". (Twenty (d|20) minutes is equivalent to two dozen (z|20) ′brevits, thirty (d|30) minutes is equivalent to three dozen (z|30) ′brevits, and so forth.) In the past, dozenalists have suggested naming this time unit the "temin", as a corruption of "ten minutes". However, deriving a name for a dozenal unit from a decimal word ("ten") and from a unit ("minute") not appearing as part of a dozenal metrology, does not seem very apt. The same argument can be leveled against a RSDN-compatible construct such as "decaminute". Instead, Primel proposes nicknaming this the ′segment. This word already has a connotation as a length of time. But consider the common decimal idiom "take ten". This means take a break of ten minutes. In a Primel world, this could be translated into "take a segment," which would mean take a break of 1 ′segment. The ′Pentquatimel (or ′Stage) The ′pentquatimel (z|105 ′timels) is equivalent to the unciaday (z|10-1 days), a dozenth of a day. This comes out to exactly d|120 minutes (z|Ӿ0 min), or two hours. In the past, dozenalists have suggested naming this time unit the "duor", as a corruption of "double hour". However, this would be just as derivative as "temin". The same argument could be leveled against a more RSDN compatible construct such as "bi-hour". A nickname for this unit that could stand on its own would be preferable. See the section on Semidays, ′Phases, and ′Stages of the Day below, for an approach to naming the ′pentquatimel. The ′Hexquatimel (or ′Day) Finally, the ′hexquatimel (z|106 ′timels) is, of course, the mean solar day. Making the day a simple dozenal power of the ′timel provides certain benefits for applications, such as astronomy, that need to relate larger amounts of time, expressed in days, to smaller amounts of time expressed in, say, ′brevits or ′jiffies. As long as dozenal quantities and Primel units are used, all that is needed is to make the proper shift of radix points. There are no extraneous factors to multiply or divide by. Relation of Primel and TGM Time Units Although TGM also considers the mean solar day a "fundamental reality", its base unit of time, the Tim, is actually a simple power of the half day, or "semiday", rather than the whole day. In fact, it is equivalent to the pentciasemiday, or z|10-5 half-days. In Primel terms, the Tim is equivalent to 6 ′timels, and the ′timel is equivalent to 2 unciaTim. Although the TGM time units are not whole dozenal powers of the ′timel, each is a simple multiple of one, so we could incorporate them into Primel as auxiliary units: Semidays, ′Phases, and ′Stages of the Day To arrive at a colloquial name for the ′pentquaday, let's first observe that we can bisect the day into two semidays, each 6 pentciadays long (equivalent to z|60 ′segments, or z|600 ′brevits, or z|10 (d|12) hours, or z|500 (d|720) minutes). But where should we make the partition? The modern Western convention, of course, is to divide the day at noon and midnight, yielding the familiar Ante Meridiem (A.M.) and Post Meridiem (P.M.) semidays. These are Latin for "Before Mid-Day" and "After Mid-Day". However, some cultures (notably the Abrahamic religions) have traditionally bisected the day at sunrise and sunset, yielding Daylight and Nighttime semidays. In Latin, these might be called Diurnum and Nocturnum. The traditional approach of these cultures is to observe the actual appearance and disappearance of the sun across the horizon, marking sunrise and sunset on a daily basis. This makes the division between Diurnum and Nocturnum, and the lengths of both, a complex, varying function of latitude, longitude, season of the year, Daylight Savings Time, and the effects of twilight atmospheric refraction. For that matter, the actual points of "mid-day", when the Sun is at zenith, and "mid-night", when the Sun is at nadir, are just as subject to daily and seasonal fluctuation. For simplicity however, Primel will assume "nominal" or "average" times for these events, with "mean sunrise" and "mean sunset" deemed to occur exactly half-way between "nominal midnight" and "nominal noon". But which way should we divide the day? Interesting question. Dozenal base provides easy divisibility by 4 -- so what if we bisected the day both ways? Then this would divide the day into quarters, analogous to the four seasons of the year or the four phases of the Moon. Primel proposes calling these quarters ′phases of the day. Each would be 3 pentciadays long (equivalent to z|30 ′segments, or z|300 ′brevits, or 6 hours, or z|260 (d|360) minutes). We can give each ′phase of the day a distinct name. One way to do this is simply to use the cross-product of the names of the two orthogonal bisections. But it turns out that English already has suitable names for these periods: Hence the semidays are combinations of two adjacent ′phases each: Note that a ′phase is actually a ′tri-pentquatimel (z|3×105 ′timels). We can further divide each ′phase into three ′stages: Early, Mid, and Late. Each ′stage would be one ′pentquatimel. Hence, a day consists of a dozen ′stages, and a ′stage consists of a dozen ′segments, or z|100 ′brevits, or d|120 minutes. In a Primel world, people would likely tell time in terms of the ′brevit count. Since the ′brevit is 5/6 of a minute, this gives accuracy to the minute and better, using only three dozenal digits. Conventional d|12-hour clock time requires four digits plus an indicator of which semiday it is, A.M. or P.M. TGM time in bictics does better in that the hour is encoded in a single digit and the top digit encodes the semiday (0=A.M., 1=P.M.). However, one more digit only gives accuracy down to the nearest 5-minute (6-′brevit) block. To get at least minute accuracy in TGM requires 4 digits. But because the bictic is half the size of the ′brevit, and only d|25 seconds long, this provides too much accuracy, at the expense of taking up an additional digit. Bottom line, the Primel scheme is the most compact. The so-called "9-to-5" job would start at z|460 ′brevits, half-way through Mid Morning stage, and would end at z|860 ′brevits, half-way through Late Afternoon stage. This gives a total duration of z|400 ′brevits or 4 ′stages (8 hours). Then again, in a Primel world, businesses might opt to start and end the work day on round stages, let's say z|400 to z|800 ′brevits. Colloquialism for Various Fractions of the Day Additional Auxiliary Primel Time Units Here are a few additional auxiliary units that are all interesting multiples of some dozenal power of the ′timel. Dozenal Perennial Calendar: Symmetry 454 A Perennial Calendar can be constructed where every year and month starts on the same day of the week and consists of a whole number of weeks, and where a leap year adds a leap week onto the end of the year, rather than a leap day in February. The pattern of leap years would be quite different, of course. When such a calendar is interpreted in dozenal, there's a nice sort of correspondence between how each month is either z|24 or z|2Ɛ days and how each year is either z|264 or z|26Ɛ days; or equivalently, how each month is either 4 or 5 weeks and how each year is either z|44 or z|45 weeks. (This is essentially a dozenalization of Irv Bromberg's Symmetry 454 Calendar.) The following calendar is completely in dozenal base. Dozenal Perennial Calendar: Symmetry 676 A variation of the Perennial Calendar would give months either z|26 or z|27 days, but would make each quarter and year a whole number of weeks, with a leap week added periodically at the end of the year. (This is essentially a dozenalization of Irv Bromberg's Symmatry 010 Calendar.) Dozenal Orders of Magnitude: Time This is a Primel version of the